1) "I answered this partly before. I was only looking for a general socioeconomic factor and did not have any specific model in mind. No hypotheses were made about any non-general factors, nor was any specific model of the data advanced beforehand. This is why I did not use CFA either."

You should mention the size of the subsequent factors, i.e., variance explained.

2) 'General factor' is still not defined in the paper. The fact that lots of the variables have negative loadings on the first factor and the implications of this fact should be discussed straight away in section 3. How many loadings have the correct sign? It would make sense to merge sections 3 and 8, because you should discuss what the loadings look like before rather than after running all those analyses using the loadings.

3) "I also ran a oblimin rotation. With nfactors=5, all factors extracted correlate with each other in the right direction (note ML2 is reversed). This indicates a general, higher-order factor, yes?"

Yes, this is evidence in favor of a general factor unlike the analyses in the paper. However, the number of factors extracted should be decided based on accepted methods (Kaiser's rule, scree plot, parallel analysis...) rather than forced on the data.

4) "Similarly, the congruence factor was 1.0."

It's the congruence coefficient.

5) In sections 4-6 the method of calculating the factor/component scores should be mentioned, and it should be clarified that when different extraction methods are compared across different numbers of variables, PCA is always compared to PCA, ML to ML, etc.

6) "These very high correlations resulting from the use of method of correlated vectors in these two datasets give indirect support for researchers who have been arguing that the heterogeneous and lower than unity results are due to statistical artifacts, especially sampling error and restriction of range of subtests"

This sentence is unclear because it is not specified what the researchers have argued. Mention g loadings, IQ, or something.

7) "There is a question concerning whether it is proper to analyze do the MCV analyses without reversing the variables that have negative loadings on the S factor first. Using the non-reversed variables means the variance is higher which increases the correlation. Reversing them would decrease the correlations. I decided to use the data as they were given by the authors i.e. with no reversing of variables. As one can see from the plots, reversing them would not substantially change the results."

Say what the MCV results are with reversed variables.

8) "The analyses carried out in this paper suggest that the S factor is not quite like g. Correlations between the first factor from different subsets did not reach unity, even when extracted from 10 non-overlapping randomly picked tests (mean r’s = .874 and .902)."

You compared factor scores, Johnson et al. compared latent factors in CFA. Different methods, so no reason to expect similar results. It is unsurprising that factor scores based on 10 variables (many with measurement scale issues to boot) are not perfectly correlated with the underlying factor because such scores, especially PCA ones, have plenty of specific and error variance in them. In contrast, CFA factors based on, say, 10 or more variables are highly stable and contain no specific/error variance. When you increase the number of variables to 40 or 50 in EFA, factor scores will be much more highly correlated with the putative underlying factor than with 10 variables. The almost-unity correlation between the SPI and DP factors is an indicator of the S factor's stability while the lower correlations using 10 variables are what you would expect regardless of the nature of the underlying factor--for example, the correlation between g scores from two IQ batteries with 10 subtests each will not be 1.00.

9) "I don't know what you mean regarding formative vs. reflective factor. Perhaps you can link to some material that covers these concepts or explain them briefly."

In reflective factor models the factor causes differences in its indicators, while in formative models the factor is non-causal and the indicators cause variance in it. The g factor is typically seen as a reflective factor (general intellectual capacity causes performance differences in cognitive tests), while SES is typically seen as a formative factor (differences in income, occupation, etc. cause differences in SES).

Is your S factor just a stalking horse for the G factor? Then you could argue that different indicators of international well-being are just "items" in an international IQ test, cf. Gordon's discussion of life events as IQ items in his "Everyday life as an intelligence test." However, I think that this analogy is awkward when the cases are countries rather than individuals, and the psychometric quality of the international IQ data is as bad as it is.

---

Your other answers/alterations are OK.

The CC paper is attached.

You should mention the size of the subsequent factors, i.e., variance explained.

2) 'General factor' is still not defined in the paper. The fact that lots of the variables have negative loadings on the first factor and the implications of this fact should be discussed straight away in section 3. How many loadings have the correct sign? It would make sense to merge sections 3 and 8, because you should discuss what the loadings look like before rather than after running all those analyses using the loadings.

3) "I also ran a oblimin rotation. With nfactors=5, all factors extracted correlate with each other in the right direction (note ML2 is reversed). This indicates a general, higher-order factor, yes?"

Yes, this is evidence in favor of a general factor unlike the analyses in the paper. However, the number of factors extracted should be decided based on accepted methods (Kaiser's rule, scree plot, parallel analysis...) rather than forced on the data.

4) "Similarly, the congruence factor was 1.0."

It's the congruence coefficient.

5) In sections 4-6 the method of calculating the factor/component scores should be mentioned, and it should be clarified that when different extraction methods are compared across different numbers of variables, PCA is always compared to PCA, ML to ML, etc.

6) "These very high correlations resulting from the use of method of correlated vectors in these two datasets give indirect support for researchers who have been arguing that the heterogeneous and lower than unity results are due to statistical artifacts, especially sampling error and restriction of range of subtests"

This sentence is unclear because it is not specified what the researchers have argued. Mention g loadings, IQ, or something.

7) "There is a question concerning whether it is proper to analyze do the MCV analyses without reversing the variables that have negative loadings on the S factor first. Using the non-reversed variables means the variance is higher which increases the correlation. Reversing them would decrease the correlations. I decided to use the data as they were given by the authors i.e. with no reversing of variables. As one can see from the plots, reversing them would not substantially change the results."

Say what the MCV results are with reversed variables.

8) "The analyses carried out in this paper suggest that the S factor is not quite like g. Correlations between the first factor from different subsets did not reach unity, even when extracted from 10 non-overlapping randomly picked tests (mean r’s = .874 and .902)."

You compared factor scores, Johnson et al. compared latent factors in CFA. Different methods, so no reason to expect similar results. It is unsurprising that factor scores based on 10 variables (many with measurement scale issues to boot) are not perfectly correlated with the underlying factor because such scores, especially PCA ones, have plenty of specific and error variance in them. In contrast, CFA factors based on, say, 10 or more variables are highly stable and contain no specific/error variance. When you increase the number of variables to 40 or 50 in EFA, factor scores will be much more highly correlated with the putative underlying factor than with 10 variables. The almost-unity correlation between the SPI and DP factors is an indicator of the S factor's stability while the lower correlations using 10 variables are what you would expect regardless of the nature of the underlying factor--for example, the correlation between g scores from two IQ batteries with 10 subtests each will not be 1.00.

9) "I don't know what you mean regarding formative vs. reflective factor. Perhaps you can link to some material that covers these concepts or explain them briefly."

In reflective factor models the factor causes differences in its indicators, while in formative models the factor is non-causal and the indicators cause variance in it. The g factor is typically seen as a reflective factor (general intellectual capacity causes performance differences in cognitive tests), while SES is typically seen as a formative factor (differences in income, occupation, etc. cause differences in SES).

Is your S factor just a stalking horse for the G factor? Then you could argue that different indicators of international well-being are just "items" in an international IQ test, cf. Gordon's discussion of life events as IQ items in his "Everyday life as an intelligence test." However, I think that this analogy is awkward when the cases are countries rather than individuals, and the psychometric quality of the international IQ data is as bad as it is.

---

Your other answers/alterations are OK.

(2014-Aug-01, 23:32:03)menghu1001 Wrote:(2014-Aug-01, 17:20:07)Dalliard Wrote: There are other sources that are more sanguine about the CC, e.g., https://media.psy.utexas.edu/sandbox/gro...ruence.pdf In any case, the problems with using Pearson's r in the analysis of factor loadings are even greater.

I can't access your link, it says :

Quote:gateway incorrect

error 502

The CC paper is attached.

**Attached Files**

Factor Congruence.pdf (Size: 166.93 KB / Downloads: 9,232)